Power corrections to αs(Mτ), |Vus| and m¯s

We re-examine recent determinations of power corrections from τ-decay and confront the results with the existing ones from QCD spectral sum rules (QSSR). We conclude that contrary to the QSSR analysis, which lead to 〈αsG2〉=(6.8±1.3)10−2GeV4, τ-decay is not a good place for extracting the gluon condensate due to its extra αs2 coefficient which suppresses its contribution in this process. Results from e+e− sum rules and τ-decay: ραs〈u¯u〉2=(4.5±0.3)10−4GeV6, where ρ=3.0±0.2 confirm the deviation from the vacuum saturation estimate of the four-quark condensate. “Non-standard” power corrections (direct instantons, duality violation and tachyonic gluon mass) beyond the SVZ-expansion, partially cancel out in the V+A hadronic τ-decay channel, which gives at order αs4: αs(Mτ)=0.3249(29)ex(75)th leading to αs(MZ)|τ=0.1192(4)ex(9)th, in remarkable agreement with (but more accurate than) αs(MZ)|Z=0.1191(27) obtained at the same αs4 order from the Z-width and the global fit of electroweak data. Finally, the rôle of the tachyonic gluon mass in the determinations of |Vus| from τ-decay and of m¯s from τ decay, e+e− and (pseudo)scalar channels is emphasized.